Chern classes of logarithmic derivations for some non-free arrangements

TL;DR

This paper investigates the relationship between Chern classes of logarithmic derivations and the Chern--Schwartz--MacPherson class for certain non-free arrangements, extending known results from free arrangements.

Contribution

It characterizes the discrepancy between these classes for locally tame arrangements with isolated non-free singularities.

Findings

Identifies the defect in equality of classes for specific arrangements.

Provides a formula for the difference in classes.

Extends previous results from free to certain non-free arrangements.

Abstract

Paolo Aluffi showed that the Chern--Schwartz--MacPherson class of the complement of a free arrangement agrees with the total Chern class of the sheaf of logarithmic derivations along the arrangement. We describe the defect of equality of the two classes for locally tame arrangements with isolated non-free singular loci.